Course detail

Linear Algebra

FP-laPAcad. year: 2026/2027

The subject is part of the theoretical basis of the field. Learning outcomes of the course unit The aim of the course is to unify and supplement the students' knowledge in the areas of further teaching of basic mathematical concepts and to teach students the comprehension of using the methods and consept  of the set theory, mathematical logic, and linear algebra (limit, cotinuity, derivative) of one variable (including basic applications in economic disciplines).

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Department

Institute of Informatics (ÚI)

Entry knowledge

Knowledge of secondary-school mathematics.

Rules for evaluation and completion of the course

Credit requirements:

Passing control tests and achieving at least 55% points or passing a comprehensive written work and achieving at least 55% points.
Awarding credit is a necessary condition for taking the exam.

Exam requirements:

The exam has a written and an oral part, with the focus of the exam being the oral part.

For all tasks in the written part, the calculation must be written down, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.


Completion of the subject for students with individual study:
Passing the comprehensive control test and achieving at least 55% points.
Awarding credit is a necessary condition for taking the exam.
The exam has a written and an oral part, with the focus of the exam being the oral part.
For all tasks in the written part, the calculation must be written down, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.

 

Participation in exercises is controlled.

Aims

Learning outcomes of the course unit the aim of the course is to learn some aspects of set theory, mathematical logic, and linear algebra (logical operations, Boolean algebra, function approximation, and solving algebraic systems of linear equations), including the realization of necessary calculations in general and in economic applications (also with respect to the use of computing).
The acquired knowledge and practical mathematical skills will in particular serve as a basis for acquiring knowledge and disseminating skills in economically oriented fields and for the correct use of mathematical software, and will be an important starting point for learning new knowledge in math mathematical subjects.

Study aids

See literature

Prerequisites and corequisites

Not applicable.

Basic literature

MEZNÍK, I. Diskrétní matematika pro užitou informatiku, Brno, CERM s.r.o., 2013. 185 s, ISBN 978-80-214-4761-5.
MEZNÍK, Ivan, 2017. Základy matematiky pro ekonomii a management. Vyd. 2., rozš. Brno: Fakulta podnikatelská Vysokého učení technického v Brně v Akademickém nakladatelství CERM, s.r.o. Brno. ISBN 978-80-214-5522-1

Recommended reading

HOFFMANN, Laurence D. a BRADLEY, Gerald L., 2007. Calculus for business, economics, and the social and life sciences. 10th ed. Boston: McGraw-Hill. ISBN 978-0-07-122024-8
JACQUES, Ian, 2023. Mathematics for economics and business. Tenth edition. Harlow, England: Pearson. ISBN 978-1-292-19166-9.
KLŮFA, Jindřich a SÝKOROVÁ, Irena, 2023. Učebnice matematiky (2) pro studenty VŠE. Jesenice: Ekopress. ISBN 978-80-87865-86-6.
MEZNÍK, I.; KARÁSEK, J.; MIKLÍČEK, J. Matematika I pro strojní fakulty, 1.vyd. SNTL, Praha, 1992. 502 s. ISBN 80–03–00313-X.

Classification of course in study plans

  • Programme BAK-MIn Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

13 hours, optionally

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Syllabus

1. Numeric sets N, Z, Q, R. Modifications of mathematical expressions, basic formulas. Numeric function and its inverse function. Graph of a function, shifts of graphs.

2. Linear, power, exponential and its inverse logarithmic function. Monotone, even and odd functions. Shifts of graphs of the above functions.

3. Trigonometric and their inverse functions. Periodicity of a function. Shifts of graphs of the above functions. Composite function.

4. Sequences of real numbers. Limit of a sequence. Basic formulas for calculating limits. Infinitely large, infinitely small, monotone and bounded sequences.

5. Arithmetic and geometric sequences and their applications in banking: Deposits, savings, loans.

6. Summary

7. Limit and continuity of a function at a point. Proper and improper limits, limits at proper and improper points. Basic formulas for calculating limits.

8. Derivative and differential of a function, meaning of the derivative, tangent equations. rules of derivation. Derivative of a composite function.

9. Use of the differential in calculating the value of a function at a point. Use of derivatives in calculating limits (L'Hôpital's rule).

10. Relationship between derivative and Monotonicity, local and absolute extrema. Finding intervals of monotonicity and extrema.

11. Higher-order derivatives, Relationship between the second derivative and convexity and concavity of a function, Inflection point. Constructing a graph of a function.

12. Summary

13. Asymptotes of a function. Course of a function - a complete description of the behavior of a function (including asymptotic properties).

Exercise

26 hours, compulsory

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Syllabus

1. Mathematical logic. Propositions, operations with propositions, compound propositions,
2. Laws of propositional logic, tautology and contradiction.
3. Boolean algebras, Boolean function. Representation of Boolean functions. Gates.
4. Cartesian product, relations between sets, relations on a set.
5. Tolerance, equivalence, ordering-I.
6. Tolerance, equivalence, ordering-II.

7. Polynomial functions. Roots of polynomials, fundamental theorem of algebra, factorization of a polynomial, determination of the root of a polynomial, Horner's scheme.

8. Approximation of functions, Lagrange's interpolation polynomial
Matrix properties, matrix operations, vector column, system of linear algebraic equations as a matrix equation. calculation of rank and inverse matrix.
9. Determinant, properties and methods of calculation.

10. System of linear algebraic equations, Frobenius theorem,

11. Gaussian elimination method of solvability of systems of linear equations-I

12. Gaussian elimination method of solvability of systems of linear equations-II

13. Kronecker theorem, solvability of systems of linear equations

Self-study

50 hours, optionally

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Individual preparation for an ending of the course

40 hours, optionally

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.